Question: Rewrite as a simplified fraction. ${2.6\overline{51} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2651.5151...\\ 10x &= 26.5151...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2625}$ ${x = \dfrac{2625}{990}} $ ${x = \dfrac{175}{66}} \text{or} {2 \dfrac{43}{66}}$